## The Complexity of Type Inference for Higher-Order Typed Lambda Calculi (1991)

Venue: | J. Funct. Programming |

Citations: | 28 - 11 self |

### BibTeX

@INPROCEEDINGS{Henglein91thecomplexity,

author = {Fritz Henglein and Harry G. Mairson},

title = {The Complexity of Type Inference for Higher-Order Typed Lambda Calculi},

booktitle = {J. Funct. Programming},

year = {1991},

pages = {119--130}

}

### Years of Citing Articles

### OpenURL

### Abstract

We analyze the computational complexity of type inference for untyped -terms in the second-order polymorphic typed -calculus (F 2 ) invented by Girard and Reynolds, as well as higher-order extensions F 3 ; F 4 ; : : : ; F ! proposed by Girard. We prove that recognizing the F 2 - typable terms requires exponential time, and for F ! the problem is nonelementary. We show as well a sequence of lower bounds on recognizing the F k -typable terms, where the bound for F k+1 is exponentially larger than that for F k . The lower bounds are based on generic simulation of Turing Machines, where computation is simulated at the expression and type level simultaneously. Non-accepting computations are mapped to non-normalizing reduction sequences, and hence non-typable terms. The accepting computations are mapped to typable terms, where higher-order types encode reduction sequences, and first-order types encode the entire computation as a circuit, based on a unification simulation of Boolean logic. ...